Step 10: Rotate Corners
There are two basic moves to rotate the corners without affecting any other pieces. They are very similar, and they both rotate two corners that are next to each other.
The first solves them when the top color is pointing “outward”, and the second solves them when the top colors are pointing in the same direction:
As you can see, the moves are the same, except the second skips the first rotation (and does it at the end instead).
These two basic moves sometimes need to be combined to rotate all of the problematic corners. Any situation you run into can be solved using just these two moves (and combinations of them):